shagalo wrote:
VeritasPrepKarishma wrote:
shagalo wrote:
can any one tell me why (1) and (2) are insufficient ?
(1) shows that the set is …. -16,-8,-4,-,2,4,8,16….( there is no 12 here) so it is sufficient.
(2) shows that the set is …. -27,-9,-3,3,9,27,…… ( there is no 12 here) so it is sufficient.
so the answer is D … each alone is sufficient.
any explanation please? thanks
How does statement 1 show that 12 is not in the set? All statement 1 tells you is that 2 is there and hence -2 is there. We don't know anything about other elements. How did you get 4, 8 etc. We are not given that if 2 is there, only powers of 2 will be there.
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Sorry but your explanation is not clear.
and i got these numbers " -16,-8,-4,-,2,4,8,16…" after applying the statement (1) on the equation (i) and (ii).
what i understood is that if you applied statement (1) "2 in K", then you will get this set of numbers " -16,-8,-4,-,2,4,8,16…" which do not include 12. the same apply on statement (2).
could you explain what is the flaw in my understanding.
Thanks
Given:
(i) If x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K
Stmnt 1: 2 is in K
This implies 2, -2, -4 (2*-2), -8 (2*-4), 8 (-2*-4), etc are in the set. 4 will not be there. But how do you know that no other elements are there in the set? Could we have a set like this: {12, 2, 24, -2, -12, -24 ...}
Does it satisfy all 3 conditions given above? Yes.
The set {2, -2, -4, -8, ...} satisfies all 3 conditions too.
Hence we don't know what the set actually looks like. Just because the set has 2 doesn't mean it cannot have 12.
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Karishma
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